Multi-fidelity Learning of Reduced Order Models for Parabolic PDE Constrained Optimization

Klein, Benedikt; Ohlberger, Mario

Research article in digital collection | Preprint | Peer reviewed

Abstract

This article builds on the recently proposed RB-ML-ROM approach for parameterized parabolic PDEs and proposes a novel hierarchical Trust Region algorithm for solving parabolic PDE constrained optimization problems. Instead of using a traditional offline/online splitting approach for model order reduction, we adopt an active learning or enrichment strategy to construct a multi-fidelity hierarchy of reduced order models on-the-fly during the outer optimization loop. The multi-fidelity surrogate model consists of a full order model, a reduced order model and a machine learning model. The proposed hierarchical framework adaptively updates its hierarchy when querying parameters, utilizing a rigorous a posteriori error estimator in an error aware trust region framework. Numerical experiments are given to demonstrate the efficiency of the proposed approach.

Details about the publication

Name of the repositoryarXiv
Article number2503.21252
Statussubmitted / under review
Release year2025
Language in which the publication is writtenEnglish
DOI10.48550/arXiv.2503.21252
Link to the full text https://doi.org/10.48550/arXiv.2503.21252
KeywordsReduced order models; multi-fidelity learning; parabolic PDE constrained optimization; trust region algorithm

Authors from the University of Münster

Klein, Benedikt Simon
Professorship of Applied Mathematics, especially Numerics (Prof. Ohlberger)
Ohlberger, Mario
Professorship of Applied Mathematics, especially Numerics (Prof. Ohlberger)
Center for Nonlinear Science
Center for Multiscale Theory and Computation